Transformations and Automatic Differentiation in Computational Thinking - Lecture 3

Explore transformations and automatic differentiation in this comprehensive lecture from MIT's Computational Thinking Spring 2021 series. Delve into general linear transformations, shear transformations, non-linear warping, rotations, and composite transformations. Learn about linear combinations of images and various function representations in mathematics and Julia programming. Discover automatic differentiation techniques for univariate and multivariate functions, and their applications in machine learning. Investigate vector-valued multivariate functions and their role in transformations. Gain insights into the significance of determinants in scaling and access additional resources for mastering automatic differentiation with Julia in just 10 minutes.

Introduction by MIT's Prof. Alan Edelman.
Agenda of Lecture0-1:30 Transformations and Automatic Differentiations.
General Linear Transformation.
Shear Transformation.
Non-Linear Transformation(Warp).
Rotation.
Compose Transformation(Rotate followed by Warp).
More Transformations(xy, rθ).
Linear and Non-Linear Transformations.
Linear combinations of Images.
Functions in Maths and in Julia(Short form, anonymous and long form).
Automatic Differentiation of Univariates.
Scalar Valued Multivariate Functions.
Automatic Differentiation: Scalar valued and Multivariate Functions.
Minimizing "loss function" in Machine Learning.
Transformations: Vector Valued Multivariate Functions.
Automatic Differentiation of Transformations.
But what is a transformation, really?.
Significance of Determinants in Scaling.
Resource for Automatic Differentiation in 10 minutes with Julia.